scholarly journals FittingC2Continuous Parametric Surfaces to Frontiers Delimiting Physiologic Structures

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Jason D. Bayer ◽  
Matthew Epstein ◽  
Jacques Beaumont
Keyword(s):  
Geometric Model ◽  
Edge Length ◽  
Mathematical Representation ◽  
Mouse Heart ◽  
Parametric Surfaces ◽  
Polygonal Mesh ◽  
Geometric Data ◽  
Segmented Images ◽  
Parametric Plane ◽  
Data Points

We present a technique to fitC2continuous parametric surfaces to scattered geometric data points forming frontiers delimiting physiologic structures in segmented images. Such mathematical representation is interesting because it facilitates a large number of operations in modeling. While the fitting ofC2continuous parametric curves to scattered geometric data points is quite trivial, the fitting ofC2continuous parametric surfaces is not. The difficulty comes from the fact that each scattered data point should be assigned a unique parametric coordinate, and the fit is quite sensitive to their distribution on the parametric plane. We present a new approach where a polygonal (quadrilateral or triangular) surface is extracted from the segmented image. This surface is subsequently projected onto a parametric plane in a manner to ensure a one-to-one mapping. The resulting polygonal mesh is then regularized for area and edge length. Finally, from this point, surface fitting is relatively trivial. The novelty of our approach lies in the regularization of the polygonal mesh. Process performance is assessed with the reconstruction of a geometric model of mouse heart ventricles from a computerized tomography scan. Our results show an excellent reproduction of the geometric data with surfaces that areC2continuous.

A Mesh Reduction Approach to Parametric Surface Polygonization

1995 ◽  
Author(s):  
M. Asif Khan ◽  
Judy M. Vance
Keyword(s):  
Computer Aided Design ◽  
Visible Region ◽  
Optimization Procedure ◽  
Boundary Edge ◽  
Parametric Surfaces ◽  
Polygonal Mesh ◽  
Surface Information ◽  
Cad Models ◽  
Aided Design ◽  
Edge Reduction

Abstract Surface polygonization is the process by which a representative polygonal mesh of a surface is constructed for rendering or analysis purposes. This work presents a new surface polygonization algorithm specifically tailored to be applied to a large class of models which are created with parametric surfaces. This method has particular application in the area of building virtual environments from computer-aided-design (CAD) models. The algorithm is based on an edge reduction scheme that collapses two vertices of a given polygon edge onto one new vertex. A two step approach is implemented consisting of boundary edge reduction followed by interior edge reduction. A maximin optimization is used to determine the location of the new vertex. The concept of a visible region as the location space of the new vertex is introduced. The method presented here differs from existing methods in that it takes advantage of the fact that for many models, the exact surface representation of the model is known before the polygonization is attempted. Because the precise surface definition is known, a maximin optimization procedure, that uses the surface information, can be used to locate the new vertex. The algorithm attempts to overcome the deficiencies in existing techniques while minimizing the number of polygons required to represent a surface and still maintaining surface integrity in the rendered model. This paper presents the algorithm and testing results.

A Point-Structured Geometric Modeling Approach to Foot Shape Representation

2012 ◽  
Author(s):  
Ming J. Tsai ◽  
Hung W. Lee ◽  
Hsueh Y. Lung
Keyword(s):  
Geometric Modeling ◽  
Shape Representation ◽  
Geometric Model ◽  
Quantitative Description ◽  
Compact Representation ◽  
Shape Information ◽  
Modeling Approach ◽  
Data Points ◽  
3D Geometric Model ◽  
Structured Representation

A compact representation for the quantitative description of foot shape is important not only for the foot measurement and anthropometry, but also for the ergonomic design of footwear. Based on foot scanned data, a novel point-structured geometric modeling approach to the reduction of 3D point cloud and the preservation of shape information is proposed. The semantic descriptions of foot features are interpreted into logical definitions. A total of fifteen feature points are thus defined. Finally, there are only a total of 2,093 data points needed in such a point-structured representation. Based on it, it is easy to fetch not only the 1D and 2D measurements, but also the 3D feature curves of the foot shape. It can provide a compact 3D geometric model to serve as a significant database for the individuals and, thereby, becomes a useful tool in investigating the foot and manufacturing the foot related apparel and devices.

scholarly journals Hypergraph Optimization for Multi-Structural Geometric Model Fitting

2019 ◽  
Vol 33 ◽  
pp. 8730-8737
Author(s):  
Shuyuan Lin ◽  
Guobao Xiao ◽  
Yan Yan ◽  
David Suter ◽  
Hanzi Wang
Keyword(s):  
Spectral Clustering ◽  
Input Data ◽  
State Of The Art ◽  
Geometric Model ◽  
Model Fitting ◽  
Synthetic Data ◽  
Estimation Algorithm ◽  
Sampling Efficiency ◽  
Data Points ◽  
Fitting In

Recently, some hypergraph-based methods have been proposed to deal with the problem of model fitting in computer vision, mainly due to the superior capability of hypergraph to represent the complex relationship between data points. However, a hypergraph becomes extremely complicated when the input data include a large number of data points (usually contaminated with noises and outliers), which will significantly increase the computational burden. In order to overcome the above problem, we propose a novel hypergraph optimization based model fitting (HOMF) method to construct a simple but effective hypergraph. Specifically, HOMF includes two main parts: an adaptive inlier estimation algorithm for vertex optimization and an iterative hyperedge optimization algorithm for hyperedge optimization. The proposed method is highly efficient, and it can obtain accurate model fitting results within a few iterations. Moreover, HOMF can then directly apply spectral clustering, to achieve good fitting performance. Extensive experimental results show that HOMF outperforms several state-of-the-art model fitting methods on both synthetic data and real images, especially in sampling efficiency and in handling data with severe outliers.

scholarly journals Pre-Processing and Surface Reconstruction of Points Cloud Based on Chord Angle Algorithm Technique

2020 ◽  
Vol 16 (3) ◽  
pp. 34-42
Author(s):  
Ali M. Albdairy ◽  
Ahmed A. A. Al-Duroobi ◽  
Maan A. Tawfiq
Keyword(s):  
Case Studies ◽  
Point Cloud ◽  
Rapid Development ◽  
Laser Scanner ◽  
Modern Technology ◽  
Mathematical Representation ◽  
Adjacent Pair ◽  
3D Objects ◽  
Laser Scanners ◽  
Data Points

Abstract Although the rapid development in reverse engineering techniques, 3D laser scanners can be considered the modern technology used to digitize the 3D objects, but some troubles may be associate this process due to the environmental noises and limitation of the used scanners. So, in the present paper a data pre-processing algorithm has been proposed to obtain the necessary geometric features and mathematical representation of scanned object from its point cloud which obtained using 3D laser scanner (Matter and Form) through isolating the noised points. The proposed algorithm based on continuous calculations of chord angle between each adjacent pair of points in point cloud. A MATLAB program has been built to perform the proposed algorithm which implemented using a suggested case studies with cylinder and dome shape. The resulted point cloud from application the proposed algorithm and result of surface fitting for the case studies has been proved the proficiency of the proposed chord angle algorithm in pre-processing of data points and clean the point cloud, where the percent of data which was ignored as noisy data points according to proposed chord angle algorithm was arrived to (81.52%) and (75.01%)of total number of data points in point cloud for first and second case study respectively.

A Method to Design Custom-Fit Stent Graft for Abdominal Aortic Aneurism

2015 ◽  
Author(s):  
Giorgio Colombo ◽  
Simone Bartesaghi ◽  
Eduardo Pallares
Keyword(s):  
Stent Graft ◽  
Cross Sections ◽  
Cfd Simulation ◽  
Design Method ◽  
Geometric Model ◽  
Endovascular Aneurysm Repair ◽  
Specific Patient ◽  
Aorta Aneurysm ◽  
Optimal Behavior ◽  
Geometric Data

Abdominal Aorta Aneurysm (AAA) affects aorta, especially above the iliac bifurcation where the Wall Shear Stress (WSS) is greater. Consequence may be fatal in case of breakage; a way to treat it is Endovascular Aneurysm Repair (EVAR) where a stent graft is placed inside the aorta without open surgery requirement. Because of the standards, stent graft can be chosen between several sizes: in some cases, this device cannot fit perfectly with the anatomy of the patient and this can lead to a not optimal behavior of the prosthesis and further complications. This study present a method to design and test specific custom-fit stent graft able to better adapt to the patient artery improving the efficiency of the prosthesis and reducing the risk of the migration of the graft as well as the fabric torn. The design method is based on a 3D geometric model of the aorta, generated from CT scan data. Centrelines and geometric data for cross sections along the aorta are the inputs necessary to define the mesh of the stent. A custom algorithm is developed to size the stent in relation to the geometric data of the specific patient; when the frame of the prosthesis is defined, a CAD-based Loft Surface has used to define surfaces between the stent rings. For the bifurcation, again CAD-based Boundary Surfaces is used. The described procedure has been also applied in a Augmented Virtual Reality simulation of the EVAR and, finally, it permits a CFD simulation to evaluate the behavior of the prosthesis inserted into the aorta.

MATHEMATICAL REPRESENTATION ON THE HUMAN ARTICULAR SURFACES WITH APPLICATION OF THE THIN PLATE THEORY

2002 ◽  
Vol 14 (06) ◽  
pp. 258-261
Author(s):  
XISHI WANG ◽  
LI-QUN ZHANG
Keyword(s):  
Thin Plate ◽  
Solid Mechanics ◽  
Plate Theory ◽  
Articular Surface ◽  
New Technique ◽  
Mathematical Representation ◽  
Surface Patches ◽  
Thin Plate Theory ◽  
Data Points ◽  
A New Technique

In this paper, a new technique is developed for representing 3-D articular surface, which is based on an analogy method with application of the thin plate theory in the solid mechanics. The method is suitable to represent the scattered data points. On the other word, it does not involve the surface patches and measuring preparation in experimentally. This means the new technique is more easy and convenient than the traditional one.

scholarly journals Quantized Residual Preference Based Linkage Clustering for Model Selection and Inlier Segmentation in Geometric Multi-Model Fitting

Sensors ◽  
2020 ◽  
Vol 20 (13) ◽  
pp. 3806 ◽  
Author(s):  
Qing Zhao ◽  
Yun Zhang ◽  
Qianqing Qin ◽  
Bin Luo
Keyword(s):  
Model Selection ◽  
State Of The Art ◽  
Geometric Model ◽  
Model Fitting ◽  
Real Data ◽  
Similarity Measurement ◽  
Iterative Sampling ◽  
Art Methods ◽  
Data Points

In this paper, quantized residual preference is proposed to represent the hypotheses and the points for model selection and inlier segmentation in multi-structure geometric model fitting. First, a quantized residual preference is proposed to represent the hypotheses. Through a weighted similarity measurement and linkage clustering, similar hypotheses are put into one cluster, and hypotheses with good quality are selected from the clusters as the model selection results. After this, the quantized residual preference is also used to present the data points, and through the linkage clustering, the inliers belonging to the same model can be separated from the outliers. To exclude outliers as many as possible, an iterative sampling and clustering process is performed within the clustering process until the clusters are stable. The experiments undertake indicate that the proposed method performs even better on real data than the some state-of-the-art methods.

Modeling of Complex Surfaces Based on Unigraphics and its Error Analysis

2011 ◽  
Vol 230-232 ◽  
pp. 649-653
Author(s):  
Yue Ping Chen ◽  
Xiao Dong Nie ◽  
Yan Hui Chen ◽  
Shi Dong Li
Keyword(s):  
Error Analysis ◽  
General Purpose ◽  
Parametric Surfaces ◽  
Complex Surfaces ◽  
B Spline ◽  
Cad Systems ◽  
Spline Surface ◽  
Modeling Errors ◽  
Data Points ◽  
Data Files

Complex surfaces have been widely used in engineering. However, the current general-purpose CAD systems do not provide the modeling method of some kinds of complex surfaces such as parametric surfaces. In this paper, complex surfaces are generated by calculating the coordinates of the data points on the surfaces, creating the data files, importing the files into UG (Unigraphics), and then making use of the surface modeling functions of this software. Taking a bicubic B-spline surface for an example, the main steps of modeling of complex surfaces are presented and the modeling errors are analyzed in detail. A test is conducted to verify this approach.

scholarly journals The Mouse Heart Attack Research Tool 1.0 database

2018 ◽  
Vol 315 (3) ◽  
pp. H522-H530 ◽  
Author(s):  
Kristine Y. DeLeon-Pennell ◽  
Rugmani Padmanabhan Iyer ◽  
Yonggang Ma ◽  
Andriy Yabluchanskiy ◽  
Rogelio Zamilpa ◽  
...  
Keyword(s):  
Myocardial Infarction ◽  
Heart Attack ◽  
Ventricular Remodeling ◽  
Left Ventricular Remodeling ◽  
Large Data ◽  
Left Ventricular ◽  
Research Tool ◽  
Mouse Heart ◽  
Data Set ◽  
Data Points

The generation of big data has enabled systems-level dissections into the mechanisms of cardiovascular pathology. Integration of genetic, proteomic, and pathophysiological variables across platforms and laboratories fosters discoveries through multidisciplinary investigations and minimizes unnecessary redundancy in research efforts. The Mouse Heart Attack Research Tool (mHART) consolidates a large data set of over 10 yr of experiments from a single laboratory for cardiovascular investigators to generate novel hypotheses and identify new predictive markers of progressive left ventricular remodeling after myocardial infarction (MI) in mice. We designed the mHART REDCap database using our own data to integrate cardiovascular community participation. We generated physiological, biochemical, cellular, and proteomic outputs from plasma and left ventricles obtained from post-MI and no-MI (naïve) control groups. We included both male and female mice ranging in age from 3 to 36 mo old. After variable collection, data underwent quality assessment for data curation (e.g., eliminate technical errors, check for completeness, remove duplicates, and define terms). Currently, mHART 1.0 contains >888,000 data points and includes results from >2,100 unique mice. Database performance was tested, and an example is provided to illustrate database utility. This report explains how the first version of the mHART database was established and provides researchers with a standard framework to aid in the integration of their data into our database or in the development of a similar database. NEW & NOTEWORTHY The Mouse Heart Attack Research Tool combines >888,000 cardiovascular data points from >2,100 mice. We provide this large data set as a REDCap database to generate novel hypotheses and identify new predictive markers of adverse left ventricular remodeling following myocardial infarction in mice and provide examples of use. The Mouse Heart Attack Research Tool is the first database of this size that integrates data sets across platforms that include genomic, proteomic, histological, and physiological data.

A Three-Dimensional Adaptive Mesh Generation Approach Using Geometric Modeling With Multi-Regions and Parametric Surfaces

2013 ◽  
Vol 13 (2) ◽  
Author(s):  
Antonio C. O. Miranda ◽  
William W. M. Lira ◽  
Joaquim B. Cavalcante-Neto ◽  
Rafael A. Sousa ◽  
Luiz F. Martha
Keyword(s):  
Finite Element ◽  
Geometric Modeling ◽  
Geometric Model ◽  
Adaptive Strategy ◽  
Parametric Surfaces ◽  
3D Finite Element ◽  
Background Structure ◽  
Advancing Front ◽  
Binary Partition ◽  
Surface Meshes

This work presents a methodology for adaptive generation of 3D finite element meshes using geometric modeling with multiregions and parametric surfaces, considering a geometric model described by curves, surfaces, and volumes. This methodology is applied in the simulation of stress analysis of solid structures using a displacement-based finite element method and may be extended to other types of 3D finite element simulation. The adaptive strategy is based on an independent and hierarchical refinement of curves, surfaces, and volumes. From an initial model, new sizes of elements obtained from a discretization error analysis and from geometric restrictions are stored in a global background structure, a recursive spatial composition represented by an octree. Based on this background structure, the model's curves are initially refined using a binary partition algorithm. Curve discretization is then used as input for the refinement of adjacent surfaces. Surface discretization also employs the background octree-based refinement, which is coupled to an advancing front technique in the surface's parametric space to generate an unstructured triangulated mesh. Surface meshes are finally used as input for the refinement of adjacent volumetric domains, which also uses an advancing front technique but in 3D space. In all stages of the adaptive strategy, the refinement of curves, surface meshes, and solid meshes is based on estimated discretization errors associated with the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes curvature information into account. Numerical examples of simulation of engineering problems are presented in order to validate the methodology proposed in this work.

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